A three-dimensional (3D) crystal has a periodic dielectric function in all three orthogonal Cartesian directions (x, y, z-axes). 3D photonic crystals are attractive for very compact waveguide devices. There are numerous ways to fabricate 3D photonic crystals (PhCs) including ion-beam milling, multi-step lithography and etching (woodpile approach), and 4 or 5-beam holography. The ion-milling and woodpile approaches are process intensive and have alignment or inter-level registration issues. Single-exposure, multi-beam holography has the advantage of being able to form PhCs in a single lithography step, but has limitations on the PhC shape and size, including interrelationships between the various periodicities that restrict the available parameter space.
Interferometric lithography (IL) is a well established technique for producing 2D, e. g. confined to a photoresist layer on a substrate with variations in the plane of the substrate but not perpendicular to the substrate plane, gratings down to a λ/4n half-pitch where λ is the exposure wavelength and n the refractive index of any immersion medium (n=1 for air). IL has a large depth-of-focus with inherent uniformity for forming large-area gratings on photoresist-coated wafers. Using IL, there is no need to use a mask or lens system to produce small pitch structures. This creates an inexpensive, large-area fabrication capability for sub-micrometer pitch periodic features.
An issue in conventional multi-beam (typically 4 or 5 beams) approaches to 3D IL is that the z-pitch is constrained by the physics of the optical configuration and is typically much larger than the (x-, y-) pitches, for cases where the exposure wavelength is much shorter than the PhC pitch. This is the usual case where the exposure wavelength is in the ultraviolet region of the spectrum while the PhC is designed for visible or infrared wavelengths. Note that throughout this disclosure the pitches will be referred to as the orthogonal (x-, y- and z-) directions notwithstanding the fact that different symmetry photonic crystals have different unit cells which may not align with these Cartesian directions.
Additionally, in conventional single exposure IL, the pitch in all three directions is a function of each of the plane-wave beam angles and the exposure wavelength. In order to obtain a photonic crystal (PhC) with the x, y, and z pitches similar to each other, the exposure beam angle θ must be as close as possible to 90°, and the exposure wavelength must be close to the desired pattern pitch dimension. For example, if the desired PhC pitch is 750 nm then the exposure wavelength needs to be ˜750 nm. This is difficult because it requires a photoresist that is sensitive at that wavelength, and if the desired pitch is changed then the photoresist and the laser source also need to be changed. Most available photoresists are designed for ultraviolet and deep-ultraviolet light, rather than for infrared light. Some applications, for example to telecommunications systems, require periodicities corresponding to infrared wavelengths, where commercial photoresists are typically not available.
Photonic crystals have many useful properties and more applications are available by combining PhCs with integrated optical waveguides. Waveguides in PhCs can guide light around sharp bends, filter light, spit or mix light into multiple waveguides, and provide optical isolators and optically coupled cavities. As a result of the confinement over long path lengths, as compared with bulk material propagation, waveguides embedded in a PhC can also exhibit non-linear optical properties that can be used for optical computing applications. Most techniques for embedding waveguides into PhC involve either forming the defects or waveguide when fabricating the PhC in a layer-by-layer fashion, or by a direct write, two-photon method used for typical holographically produced PhCs. In all cases the embedded waveguide formation is a tedious and slow process.
Chiral, coil-spring-like helical photonic crystal structures, are useful for optical applications including: circular polarizers, optical diodes, and optical isolators. A chiral material lacks any planes of mirror symmetry, and is characterized by a cross coupling between the electric and the magnetic material response. This results in breaking the degeneracy between the two circularly polarized waves; i.e., the refractive index is increased for one circular polarization and reduced for the other. This gives rise to interesting phenomena that are not available from conventional materials including the possibility of a negative refractive index for one circular polarization while the refractive index for the other circular polarization remains positive.
Traditionally helical structures have been formed using either glancing angle deposition (GLAD), a technique based on physical vapor deposition that employs oblique angle deposition conditions, or serial direct laser writing based on multi-photon absorption. Both of these techniques are slow and insuitable for fabricating helical structures over large areas.